I have a categorical variable comprising of values from 1 to 7 with these probability:
score 1 2 3 4 5 6 7 p 0.01 0.01 0.03 0.05 0.2 0.3 0.4
In two different samples from the two different populations, I found the same value for 10th percentile (i.e. 4) in observed data. I want to find the likelihood of having exactly the same value for 10th percentile.
FYI, the scores are answers to a scale and probabilities are proportions for each category in a normative sample.I want to be able to do this in R.
P.S.: any suggestion on calculating cumulative distribution of a variable with above-mentioned properties is appreciated.